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The existence and global exponential stability of periodic solution for a neutral coupled system on networks with delays

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  • Zhang, Xinhong
  • Li, Wenxue
  • Wang, Ke

Abstract

In this paper, we establish sufficient conditions for the existence and global exponential stability of periodic solution to a type of neutral coupled system on networks with delays. The key to prove the existence of periodic solutions is using the combined method of graph theory, coincidence degree theory and Lyapunov functional method. And the sufficient conditions are easy to be checked. Finally, a numerical simulation is carried out to show the correctness of our main results.

Suggested Citation

  • Zhang, Xinhong & Li, Wenxue & Wang, Ke, 2015. "The existence and global exponential stability of periodic solution for a neutral coupled system on networks with delays," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 208-217.
    • Handle: RePEc:eee:apmaco:v:264:y:2015:i:c:p:208-217
    DOI: 10.1016/j.amc.2015.04.109
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    References listed on IDEAS

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    1. Dai, Yang & Cai, Yunze & Xu, Xiaoming, 2008. "Synchronization criteria for complex dynamical networks with neutral-type coupling delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(18), pages 4673-4682.
    2. Liu, Hui & Chen, Juan & Lu, Jun-an & Cao, Ming, 2010. "Generalized synchronization in complex dynamical networks via adaptive couplings," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(8), pages 1759-1770.
    3. Chen, Hao & Sun, Jitao, 2012. "Stability analysis for coupled systems with time delay on networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 528-534.
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    Cited by:

    1. Manickam Iswarya & Ramachandran Raja & Grienggrai Rajchakit & Jinde Cao & Jehad Alzabut & Chuangxia Huang, 2019. "Existence, Uniqueness and Exponential Stability of Periodic Solution for Discrete-Time Delayed BAM Neural Networks Based on Coincidence Degree Theory and Graph Theoretic Method," Mathematics, MDPI, vol. 7(11), pages 1-18, November.
    2. Han, Siyu & Hu, Cheng & Yu, Juan & Jiang, Haijun & Wen, Shiping, 2021. "Stabilization of inertial Cohen-Grossberg neural networks with generalized delays: A direct analysis approach," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    3. Liu, Yan & Guo, Ying & Li, Wenxue, 2016. "The stability of stochastic coupled systems with time delays and time-varying coupling structure," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 507-520.

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